Badosa posted on social media that the injury has forced her to shut down her season.
Ekaterina Alexandrova advanced to the last eight.
The former champion's choice of wardrobe for Monday's first-round match landed her in a spot of bother amid windy conditions
The 21-year- became the first high-profile woman player to opt out of the Australian Open -- the opening major of 2022 -- due to mental health issues arising from "quarantining".
Rafael Nadal, Dominic Thiem, Stan Wawrinka, Nick Kyrgios, Serena Williams and Simona Halep have already announced their decisions to skip the pandemic-delayed Olympics.
The No. 1-ranked Barty won her second successive Miami title, and the Australian was already in control of the match when Andreescu turned her right foot while hitting a forehand and sprawled to the hard court.
Eighth seed Andreescu, one of the 72 players unable to train during hard quarantine in the lead-up, attacked with her typical abandon at Rod Laver Arena but found a brick wall in the form of the double-handed Hsieh.
Women's world No. 1 Ashleigh Barty, Svetlana Kuznetsova, Elina Svitolina and Kiki Bertens have already decided against playing in the US Open amid the COVID-19 pandemic.
Andreescu beat Serena Williams 6-3, 7-5 in Saturday's final to maintain a 13-match unbeaten run, where she also won the Canadian Open, to break into the top 10 for the first time in her career.
The hashtag #SheTheNorth shot to the top of Canada's trending topics on Twitter, as social media users reimagined the "We the North" slogan used by the Toronto Raptors during their NBA championship-winning run.